关键词: 完全四阶非线性边值问题, 正解, 存在性, 唯一性, Leray-Schauder不动点定理, Nagumo型条件

Abstract: By using Leray-Schauder fixed point theorem, we study a class of fully fourth-order nonlinear ordinary differential equations. The existence and uniqueness of the positive solutions are proven under the condition that the nonlinear term f grows at most linearly. Under the condition that f satisfies the superlinear growth, the existence of positive solutions are obtained by introducing a Nagumo-type condition to limit that f(t,x₀,x₁,x₂,x₃) is quadratical growth on x₃ at most.

Key words: fully fourth-order nonlinear boundary value problem, positive solution,  , existence,  , uniqueness, Leray-Schauder fixed point theorem, Nagumo-type condition